標題: 製程能力指標推薦最小值及製程能力判定程序之研究
A Study of the Recommended Minimum Values of Process Capability Index and the Testing Procedure of Process Capability
作者: 盧昆宏
Kuen-Horng Lu
張保隆
Pao-Long Chang
管理科學系所
關鍵字: 製程能力指標;推薦最小值;製程能力判定程序;Process Capability Index;Recommended Minimum Values; Testing Procedure of Process Capability
公開日期: 1994
摘要: 一個製程可以被改善之前必需先建立其製程能力分析(Githow et al (1989)), 因此, 製程能力指標是品質管制及品質改進中重要的測量方法 之一 (Porter et al (1990))。且製程能力指標 (PCI) 之資訊有助於達 到下列之功能 : (1) 決定製程界限, (2) 設定標準和規格, (3) 評估製 程是否達到預期之能力。由於大部份的人僅是從樣本的 PCI 之計算值就 來判定製程是否合乎能力水準, 這是較不科學的 (Chang (1992)), 所 以, 為了降低對製程能力的誤判, 本文係先利用統計方法推導出 $\widehat {C_{pm}}$, $\widehat {C_{pmk}}$ 指標的推薦最小值, 再透 過該兩推薦最小值分別提出一套判定製程是否已達到能力水準與否的程 序, 而且該程序適合任何信賴水準, 樣本數更不必查任何圖表, 俾使得由 製程能力分析所獲得的資料更具客觀, 正確。此外, 於從事製程能力分析 時, 必需先測量產品品質之期望值, 變異數等參數。然而, 在實務上品質 特性之母體分配不一定是常態分配, 因此, 於從事製程能力分析時若對於 非常態之母體仍然假設為常態分配的話, 則會造成不正確的評估製程能 力(Rodriguez (1992))。鑑於此, 本論文乃嘗試利用百分位的方法來導出 各項製程能力指標之估計量, 以避免由於分配假設錯誤而造成計算出來的 製程能力指標之估計量是不正確之情形。綜合上述兩種情況, 建構出一製 程能力判定之程序, 該程序首先檢定母體是否具常態分配, 若母體具常態 分配則利用推薦最小值來判定製程能力,若母體不具常態分配則使用百分 位法來計算製程能力指標。 A process must have an established process capability before it can be improved (Gitlow et al(1989)), Consequence,the process capability indices (PCI) are key measures in the context of never-ending improvement in quality. Besides, the information of process capability analysis can achieve the following thing : (1) management know the process capability and can predict performance, cost, quality level; (2) management can determine the product specifications and standards; (3) management can evaluate whether a process is capabe. However, most prople simply look at the value of the PCI calculated from the given sample and make a conclusion on whether the given process is capable or not. This is not a very scientific approach (Cheng (1992)). So, in this paper uses a statistical approach to derive the recommended mininum value (RMV) of $\widehat {C_{pm}}$ and $\widehat {C_{pmk}}$, and apply the RMV method to propose a testing procedure to make a decision in assessing the capability of the process, and it allows for testing at arbitrary confidence level and sample size without any tables or figures. Besides, In most quality assurance and statistical literature, distributional and inferential properties of these indices are investigated under the assumption that the process measurements arise from a normal distribution $N(\mu, \sigma^2)$. Since process mean $\mu$ and process variance $\sigma^2$ are unknown paramenters, they are usually estimated from the sample statisiics $\overline x$ and $s^2$. As discussed by Rodriguez (1992) when non-normality occurs in process data,the calculated values of PCIs may provide an incorrect assessment of process performance if they are not interpreted properly. In this paper propose a percentile method for calculating PCIs without using any statistical tables, or calculating skewness and kurtosis of the distribution.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT830457001
http://hdl.handle.net/11536/59424
Appears in Collections:Thesis